Lesson 1
Objective: Understand equal groups of as multiplication
Application Problem (10 minutes)
There are 83 girls and 76 boys in the third grade. How
many total students are in the third grade?
Note: Students may choose to use a tape diagram or a
number bond to model the problem. They are also likely to
solve today’s application problem in less than 10 minutes.
Ten minutes have been allotted in order for you to review
the RDW (Read, Draw, Write) procedure for problemsolving.
Directions on the Read, Draw, Write (RDW) Process: Read
the problem, draw and label, write a number sentence,
and write a word sentence. The more students participate
in reasoning through problems with a systematic
approach, the more they internalize those behaviors and
thought processes.
Lesson 2
Objective: Relate multiplication to the array model.
Application Problem (5 minutes)
Jordan uses 3 lemons to make 1 pitcher of lemonade. He
makes 4 pitchers. How many lemons does he use
altogether? Use the RDW process to show your solution.
Note: This problem reviews equal groups multiplication
from Lesson 1. It also leads into today’s concept
development of relating multiplication to the array model.
Lesson 3
Objective: Interpret the meaning of factors─the size of the
group or the number of groups.
Application Problem (5 minutes)
Robbie sees that a carton of eggs shows an array with 2
rows of 6 eggs. What is the total number of eggs in the
carton? Use the RDW process to show your solution.
Note: This problem reviews writing multiplication
sentences from arrays learned in Lesson 2. The egg carton
provides a natural array for students to see 2 rows of 6.
Lesson 4
Objective: Understand the meaning of the unknown as the
size of the group in division.
Application Problem (5 minutes)
The student council holds a meeting in Mr. Chang’s
classroom. They arrange the chairs in 3 rows of 5. How
many chairs are used in all? Use the RDW process.
Note: This problem reviews relating multiplication to the
array model from Lesson 2. Students may choose to solve
by drawing an array (Lesson 2) or a number bond (Lesson
3) where each part represents the amount of chairs in
each row.
Lesson 5
Objective: Understand the meaning of the unknown as the
number of groups in division.
Application Problem (7 minutes)
Stacey has 18 bracelets. After she organizes the bracelets
by color she has 3 equal groups. How many bracelets are
in each group?
Note: This problem reviews the meaning of the unknown
as the size of the group in division from Lesson 4. It also
provides a comparison to Cynthia’s party problem in
Problem 1 of the concept development, where the
unknown represents the number of groups in division
Lesson 6
Objective: Interpret the unknown in division using the
array model.
Application Problem (6 minutes)
20 children play a game. There are 5 children on each
team. How many teams play the game? Write a division
sentence to represent the problem.
Note: This problem reviews division from Lesson 5 where
the unknown represents the number of groups. It also
leads into problem 1 of today’s lesson as it relates division
to the array model.
Lesson 7
Objective: Demonstrate the commutativity of
multiplication and practice related facts by skip-counting
objects in array models.
Application Problem (5 minutes)
Anna picks 24 flowers. She makes equal bundles of flowers
and gives 1 bundle to each of her 7 friends. She keeps a
bundle for herself too. How many flowers does Anna put
in each bundle?
Note: This problem reviews equal groups division from
Lesson 5 where the unknown represents the size of the
group. The problem’s complexity is in understanding that
the flowers are divided equally into 8 bundles, not 7, since
they need to count Anna. Students may choose to solve by
drawing a division array learned in Lesson 6 or a number
bond learned in Lesson 3.
Lesson 8
Objective: Demonstrate the commutativity of
multiplication and practice related facts by skip-counting
objects in array models.
Application Problem (10 minutes)
Children sit in 2 rows of 9 on the carpet for math time. Erin
says, “We make 2 equal groups.” Vittesh says, “We make 9
equal groups.” Who is correct? Explain how you know
using models, numbers, and words.
Note: This problem reviews the commutativity of
multiplication introduced in Lesson 7 and prepares
students for day 2 on the same concept lesson.
Lesson 10
Objective: Model the distributive property with arrays to
decompose units as a strategy to multiply.
Application Problem (5 minutes)
A guitar has 6 strings. How many strings are there on 3
guitars? Write a multiplication sentence to solve.
Note: This problem leads into today’s concept
development. Students will compare their multiplication
equation with the new equations presented in the lesson.